Graphical Synthesis of Fourbar Mechanisms by Three-Position, Instant-Center Specification

Abstract

In four-bar mechanism synthesis, solutions to both the three-position and four-position synthesis problems are well-known. However, certain practical synthesis problems also require consideration of the instantaneous center of velocity for one of the precision positions. Examples are the double-wishbone front suspension of an automobile (camber in jounce and rebound, along with roll center), and four-bar prosthetic knee (standing stability, flexion length, and sitting cosmetic advantage). Because specifying the location of the instant center constrains the solution by one free choice per dyad, it reduces the number of free choices available in a three-position problem from two to one. Thus, center point and circle point solutions to the three-position, instant center specified synthesis (TPICS) problem are located along point-pair solution curves similar to the Burmester curves in four-position synthesis. The purpose of this paper is to present a direct, graphical method for finding pivot locations in three-position, instant-center synthesis of four-bar mechanisms. The method uses pole triangle theory to determine pivot locations along center point and circle point curves. A summary of a previously-presented computational method is included. As an example, both the graphical and the computational method are used to generate TPICS center-point curves for an automotive front suspension.